Why don't you ask this on all קרבנות ציבור?
What does korbon tamid atone for?
[How would "fathers, brothers, husbands" help?].

What other karbon does the same thing (atone for women — but not men — without their participation)?

KT atones for going to Beis HaMikdosh in a state of tumah.

One might say that a woman's male relative's paying half-shekel counts for her as well. But that can't be true for a woman who doesn't have relatives. One can argue that all Jews are cousins, if you go far enough, but not a giyoret who is single.